The Federal Reserve, the powerful entity that steers the United States economy, has plenty of critics in Washington, but the White House typically holds its tongue.

Is that now changing?

When asked last week if the Fed might undermine the economy with too many interest rate increases, Larry Kudlow, the director of President Trump’s National Economic Council, said he hoped the central bank would “move very slowly.”

Last month, Fed policymakers signaled that they may make four interest rate increases this year, up from the three they previously expected. That means the Fed could raise rates two more times this year, and three next, according to the policymakers’ indications. Mr. Kudlow’s remarks could be construed as a signal that the White House does not want those increases to come quickly.

That the president’s top economic adviser expressed an opinion on monetary policy might not seem controversial, especially when so many other economic matters are up for discussion. But it had become something of a norm for the White House to refrain from questioning the Fed.

The central bank has the power to influence the economy like no other government entity. Presidents in the past leaned on the Fed to rev up growth ahead of elections, sometimes causing havoc later. Such messes persuaded White House officials to back off, and in the last two decades they have largely left the Fed to do its job. But now, with President Trump questioning so much of the existing economic order and sometimes breaking protocol, as he did last month when signaling strong jobs numbers before their release, investors and others are on the lookout for any encroachment on the Fed’s autonomy.

But in a phone interview, Mr. Kudlow said he merely was expressing his personal opinions. “I respect the Fed’s independence. In no way would I ever seek to undermine it,” he said. “I happen to approve of the Fed’s policy.”

Still, evidence is accumulating that the Trump administration might be more willing to question the central bank’s actions. “The Fed’s going to do what it has to do, but I hope they don’t overdo it,” Mr. Kudlow said in March, after it was announced that he was joining the White House.

In April, Mr. Trump made an indirect reference to the Fed’s recent conduct of monetary policy. In a tweet on the dollar’s value, he noted that “the U.S. keeps raising interest rates.”

Kevin Warsh, a former Fed governor who was a candidate to be the Fed’s chairman, came away from his interview last year with Mr. Trump with the impression that the president was not particularly mindful of central bank independence.

“In some sense the broader notion of an independent agency, that’s probably not an obvious feature to the president,” Mr. Warsh told Politico. Jerome H. Powell got the chairman’s job.

Investors, who watch interest rates closely, do not yet appear to believe that the Trump administration has crossed the line. But if Trump administration officials made a habit of questioning the Fed’s moves, investors would become unsettled, said Jim Vogel, a strategist at FTN Financial.

“The market can tolerate boundary skirmishes on monetary policy,” he said, “but it will not welcome constant skirmishes.”

The Fed’s so-called dual mandate is to foster the economic conditions that will lead to maximum employment and stable prices. It cuts interest rates to stimulate economic activity and raises them to cool the economy if there are signs that prices are rising too fast.

But the Fed’s rate increases have in the past caused growth to slow markedly, and even tipped the economy into recession. And a lackluster economy with weak jobs growth is the last thing politicians want in the lead-up to a re-election battle. That is why President George Bush in 1992 called on the Fed to cut interest rates.

Still, there is a chance that the Fed will be able to raise interest rates this year and next without causing a full-blown recession. If that happens, the Fed most likely will be able to go about its business without interference.

“Respect for Fed independence is nearly always conditional on the shape of the economy,” said Sarah Binder, a professor at George Washington University who co-wrote a book on Congress’s relations with the Fed.

The Fed may be able to avoid slamming on the brakes because the economy could be less prone to inflation than it was. Changes in the economy and the United States work force appear to have weakened the relationship between unemployment and prices.

Mr. Kudlow contends that Mr. Trump’s economic policies, like tax cuts and deregulation, are lowering costs for businesses and creating incentives for them to invest. These so-called supply-side changes, he asserts, are starting to enable the economy to grow with less risk of inflation.

This was his basis for his comments last week on the pace of rate increases, which were made in an interview with Maria Bartiromo of Fox Business. “My hope is that they understand that, and they will move very slowly,” Mr. Kudlow said, referring to the Fed.

But some economists say the tax cuts will help stoke inflation because they were enacted just as the economy was picking up steam.

The big question is how the Trump administration might react if the Fed does cause the economy to slow considerably. To apply real influence over the Fed, past administrations have gone beyond jawboning, said Sebastian Mallaby, a fellow at the Council on Foreign Relations and author of a biography of Alan Greenspan, a former Fed chairman. Past presidents have tried to put people on the Fed’s board who share their views on monetary policy or other matters. There are currently four open spots on the Fed’s board. Two of them could be filled soon.

“I’d say the Trump team is the first time in a quarter of a century when you’ve had a direct threat from a president or an administration to the independence of the Fed,” Mr. Mallaby said.

Mr. Kudlow, however, said he agreed with the Fed’s current monetary policy, because, in his view, Mr. Powell is also likely to be wary of raising interest rates too quickly. “This is what they’re doing, basically, as I understand it from Jay’s comments, public comments,” Mr. Kudlow said, referring to Mr. Powell.

A version of this article appears in print on , on Page B3 of the New York edition with the headline: A Norm-Breaking White House Keeps Its Eye on a Hawkish Fed. Order Reprints | Today’s Paper | Subscribe